The Formal Solutions for Fokker-Plank Equation of the Degenerate Optical Parametric Ampilifers in the Dissipative Systems
|School||Northeast Normal University|
|Keywords||degenerate optical parametric amplifiers ordered boson operators Fokker-Planck equation Green function|
A degenerate optical parametric amplifier(DOPA)is a phasesensitive light amplifier, and its gain depends on the optical phase difference between the pump and the input signal fields. The degenerate optical parametric amplifier is a device that provides a nonlinear coupling between two modes of the radiation field. The device itself converts light at frequency 2ω,the pump, to light at frequencyω,the signal. Modeling of practical DOPA’s is crucial for both understanding the spatial properties of the generated squeezed field, and also designing experiments aimed at generating large levels of squeezing. In long-distance fiber-optic transmission systems, optical amplifiers have become more and more indispensable. The theoretical and experimental study of fiber optical parameter amplifier has received in the past years a renewed interest after making progress in the level of apparatus, especially photonic crystal fiber which is a highly nonlinear fiber whose dispersion can be adjusted.In this paper we introduce ordered boson operators, and the theory of a thermal reservoir in quantum optics. On the basis of these theories, we investigate a special optical parametric amplifier which is so-called degenerate optical parametric amplifier. We obtain the master equation of degenerate optical parametric amplifier in the dissipative systems. If reduced density operators were superseded by c-number function, we can study the quantum statical properties of the degenerate optical parametric amplifier in a c-number domain, and obtain the operator equation of motion in a c-number domain(Fokker-Planck equation) using the property of ordered boson operators. We solve the Fokker-Planck equation for the degenerate optical parametric amplifier by two different methods. This technique can provide a simple but effective calculational methods for complicated systems.